矫情 (jiao qing) is used to describe someone who intentionally does stuff to obtain the pity or empathy from another individual.
娇气 (jiao qi) is used to describe someone who is fragile (in a derogatory manner); someone who is unable to tolerate any suffering or pain. This is also commonly used to refer to people who has the 'princess' attitude whereby everything is their life has been done for them and thus are unable or unwilling to fend for themselves.
An interesting thing to note between 矫 and 娇 is the character on their left.
For 矫, it has 矢 character which means arrow. This, thus, has a more aggressive meaning to it. Like an arrow, it refers to intentional actions done by the user.
For 娇, it has the 女 character which means female. This suggests that someone that is fragile like since females in ancient China was commonly seen as the weaker sex and had to be taken care of in a male-dominated society.